JEE Previous Year Questioncot−1(2⋅12)+cot−1(2⋅22)+cot−1(2⋅32)+… up to ∞=Topic: JEE PYQAnswer: C. Full step-by-step solution below.Aπ/2Bπ/5Cπ/4Dπ/3Correct answer: CSolution(c) cot−1(2⋅12)+cot−1(2⋅22)+cot−1(2⋅32) +… upto ∞=∑n=1∞cot−1((2n+1)−(2n−1)(2n+1)(2n−1)+1)=∑n=1∞(cot−1(2n−1)−cot−1(2n+1))=(cot−11−cot−13)+(cot−13−cot−15)+(cot−15−cot−17)+…=cot−11−cot−1∞=4π−0=4πMore Inverse Trigonometric Functions PYQsIf…The sum of the infinite series…For non-negative integer n, let……If y=cos(3π+cos−12x), then (x−y)2++3y2 is eq…